Several end{itemize}In this paper, we introduce an algorithm which

Several algorithms have been created to form partitions in a graph cite{berkhin2006survey, ng1994cient, huang1997fast, ding2001min, slota2014pulp} which contain a certain set of marked nodes. These algorithms create a subgraph known as a minimum spanning tree or an arborescence cite{kruskal1956shortest, prim1957shortest}. Dot2Dot algorithm cite{akoglu2013mining} efficiently finds the minimum arborescence of a graph with marked nodes. However, to add another marked node to this subgraph requires the algorithm be rerun with the union of the sets of marked nodes. This leads to unnecessary reiteration of operations with a large time complexity. No algorithm could be found which allows for the addition of new nodes to a partition without the reproduction of all computation steps.Generally algorithms similar to Dot2Dot have five approaches. They all are used to find the set of trees with minimum total cost on marked nodes. egin{itemize} item Finding Bounded Path Length: Finding shortest path between terminal nodes using BFS-like expansion till the threshold path length, $log|V|$ (where $|V|$ indicates the total number of vertices in graph), is reached. item Connected Components: The algorithm detects connected components and puts all directly connected terminal nodes in one group. Nodes which do not satisfy both properties are placed into separate groups. item Minimum Arborescence: The algorithm uses the transitive closure graph of terminals to find the minimum cost graphs. The algorithm calculates bounded path lengths and connected components. item 1-Level Tree: The algorithm returns a forest of Steiner trees by building a level 1 tree from the transitive closure graph by considering each terminal node as root to find the shortest path on transformed graph.  item 2-Level Tree: This algorithm generalizes 1-level tree algorithm to k-level trees. This is achieved by reducing the cost of 1-level trees successively in each step. end{itemize}In this paper, we introduce an algorithm which allows for quick addition of new marked nodes to a partition. We illustrate the success of our algorithm by providing example datasets and corresponding output. Finally, we present the relative run times between our algorithm and the original Dot2Dot to express the reduction in time complexity.